Resonance absorption by a charged damped oscillator is a standard part of freshman physics, and forms an important part of the work of physicists and engineers.
Collection pythagoraspublishing; additional_collections
The standard derivation of the expression for energy absorption by a charged damped oscillator in a uniform, homogeneous and isotropic black body field can be found in any standard textbook. The system can be considered having a coupling to a source and a response function.
In terms of the dispersion of the system, we have a spectrum of Amplitude contributions Ap with phases lagging and leading the peak angular frequency. The sum of these leading and lagging amplitude terms contribute to the total power of the system (as required by quantum mechanics).
If one were to view the Response term R, as a Dressing Transformation, then the implication of the summation of the amplitude terms in the dispersion is of some importance.
In the second article in this series, will look at Dressing Transformations in the electron and quark systems and its implication on self-energy.